Algebra Problems

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We know Algebra is one of the main things in math. We can say Algebra is the study of rules of operations and relations. We have many branches of Algebra; those are Elementary Algebra, Linear Algebra, pre Algebra, Modern Algebra and Boolean algebra. In algebra to simplify and use the different types of operations, we follow a rule that is termed as PEMDAS. Here,

P stands for Parenthesis

E stands for exponents

M stands for Multiplication

D stands for division

A stands for Addition

S stands for Subtraction.

Example 1: Evaluate [6 – (3 – 6 (6 – 4) + 7)] + 3.

Solution: To simplify this, we can use the PEMDAS rule. First we can do the operation in the parenthesis.

= [6 – (3 – 6 (6 – 4) + 7)] + 3

= [6 – (3 – 6(2) + 7)] + 3

 Now we can do the multiplication

= [6 – (3 – 12 + 7)] + 3

 = [6 + 2] + 3 = 10
 
Example 2: Solve (x-4) /3 = (x+5) /2

Solution: To solve this we can do the cross multiplication, that is
 
 2 (x – 4) = 3 (x + 5)     
 
ð  2x – 8 = 3x + 15

We can write this as

ð        3x + 15 = 2x – 8

We can add – 2x on both sides

ð  3x + 15 – 2x = 2x – 8 – 2x
 
ð  (3x – 2x) + 15 = - 8
 
ð  x + 15 = - 8

We can add – 15 on both sides of the equation

ð  x + 15 – 15 = - 8 – 15

ð  x = - 23
 

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